Particle image velocimetry (“PIV”), including digital particle image velocimetry (“DPIV”), has become a widely used quantitative flow visualization technique in fluid mechanics research due to its ability to provide non-intrusive, highly resolved measurement of planar velocity fields. With the use of ever-advancing CCD cameras, digital data acquisition systems, and sophisticated algorithms, DPIV continues to evolve and flourish. One of the key advancements is the development of Three-Dimensional Defocusing Particle Image Velocimetry (“3DDPIV”), which allows for three-dimensional velocity measurements within a volume. First proposed and established by Willert and Gharib (Willert, C. E., and M. Gharib, “Three-Dimensional Particle Imaging With a Single Camera,” Exp. Fluids 12:353-358, 1992), this technique uses the defocusing concept to obtain a particle's position in three dimensions. Using a three-lens/CCD setup and a cross-correlation algorithm on sequential images, Pereira et al. (Pereira, F., et al., “Defocusing Digital Particle Image Velocimetry: A 3-Component 3-Dimensional DPIV Measurement Technique. Application to Bubbly Flows,” Exp. Fluids 29:S78-84, 2000) mapped the bubbly flow field about a propeller using this concept. An error analysis with an uncertainty test was also reported. A two-dimensional theoretical basis of the optical design and velocity estimation methodology, together with a multi-surface refraction correction scheme, is later reported in Pereira F., and M. Gharib, “Defocusing Digital Particle Image Velocimetry and the Three-Dimensional,” 2002. Kajitani and Dabiri established a full three-dimensional characterization of the 3DDPIV system and its associated geometric uncertainty (Kajitani, L., and D. Dabiri, “A Full Three-Dimensional Characterization of Defocusing Digital Particle Image Velocimetry,” Meas. Sci. Technol. 16:790-80, 2005). Yoon and Kim adapted the defocusing concept and applied it to a micro-scale channel flow over a backward-facing step and obtained a time-averaged flow field (Yoon, S. Y., and K. C. Kim, “3D Particle Position and 3D Velocity Field Measurement in a Microvolume Via the Defocusing Concept,” Meas. Sci. Technol. 17:2897-2905, 2006). Since their microscope's lens had multiple elements, they could not directly use the 3DDPIV relations established by Kajitani and Dabiri, which were based on a single-element lens. They therefore developed a calibration-based method to determine the depth location. Pereira et al. proposed a calibration procedure to approximate the multi-element lens optical system to a single-element lens system model, thereby overcoming the difficulty of determining the depth location (Pereira, F., et al., “Microscale 3D Flow Mapping With mDDPIV,” Exp. Fluids 42:589-599, 2007). They then applied the single-lens concept to image a micro-volume 3D flow of an evaporating water droplet.
Initial implementations of 3DDPIV require three separate, yet properly coordinated, imaging systems integrated as a single unit to overcome the identification problem of overlapping particle exposures. This configuration is designed to image a large volume of interest because separating the three pinhole apertures into three individual lens/CCD systems makes it possible to increase the pinhole separation without using a costly customized large lens. Using this three-camera 3DDPIV system to measure velocities within small-scale flow fields has two major difficulties. First, due to its size and complexity, this type of system is hard to setup and calibrate. Second, with the presence of the pinhole mask, a high intensity light source is required to adequately illuminate the flow, which can noticeably heat and evaporate the fluid, thereby affecting the flow.
Efforts to avoid such difficulties in measuring flows within small volumes eventually lead to the original single camera configuration proposed by Willert and Gharib in 1992, which has been used by Yoon and Kim (2006) and Pereira et al. (2007).
The concept of the single camera 3DDPIV system is illustrated by a three-dimensional representation of the imaging system in FIG. 1 (Prior Art), which shows a particle 15 disposed on a fluid test region on one side of a lens place 20 having a mask defining three pinhole apertures 25. An imaging plane, or CCD plane 35, is disposed along the optical axis 12 opposite the test region. Light 10, reflecting from particles (e.g., particle 15) between the plane of focus (not shown, to the right of particle 15 in FIG. 1) and the lens plane 20 (the defocused region), passes through the pinholes 25 and forms triple exposures 30 (triplets) on the CCD plane 35. The size of the triplet depends on the location of the particle 15 within the defocused region. However, the system is difficult to use when the particle density becomes large due to overlapping triplet exposures, because the triplets become difficult to identify, separate, and use for particle identification. Furthermore, the necessity of the pinholes 25 has the unfortunate consequence of severely reducing the amount of light that exposes the CCD. Thus, a high intensity illumination source is needed.
There is a need, therefore, for a solution that overcomes the difficulties discussed above.